Abstract

Social network analysis emerged as an important area in sociology in the early 1930s, marking a shift from looking at individual attribute data to examining the relationships between people and groups. Surveying many different types of real-world networks, researchers quickly found that different types of social networks tend to share a common set of structural characteristics, including small diameter, high clustering, and heavy-tailed degree distributions. Moving beyond real networks, in the 1990s researchers began to propose random network models to explain these commonly observed social network structures. These models laid the foundation for investigation into problems where the underlying network plays a key role, from the spread of information and disease, to the design of distributed communication and search algorithms, to mechanism design and public policy. Here we focus on the role of peer effects in social networks. Through this lens, we develop a mathematically tractable random network model incorporating searchability, propose a novel way to model and analyze two-sided matching markets with externalities, model and calculate the cost of an epidemic spreading on a complex network, and examine the impact of conforming and non-conforming peer effects in vaccination decisions on public health policy.

Throughout this work, the goal is to bring together knowledge and techniques from diverse fields like sociology, engineering, and economics, exploiting our understanding of social network structure and generative models to understand deeper problems that — without this knowledge — could be intractable. Instead of crippling our analysis, social network characteristics allow us to reach deeper insights about the interaction between a particular problem and the network underlying it.